see the discussion in [1]}. As shown again in [1]},
the Chebyshev coefficients \(v_{n}\) , \(n=0,1,\ldots ,N\)  can be computed
efficiently via a fast cosine transform which is closely related to
the fast Fourier transform. It is also known that the Chebyshev
coefficients for a function analytic on \([-1,1]\)  decrease
exponentially, and that the numerical error in approximating a
function \(\tilde{v}\)  via (REF ) is of the order of the first
omitted coefficients \(v_{n}\)  in the Chebyshev series.
